Question

# You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.       Ho:p1=p2Ho:p1=p2       H1:p1<p2H1:p1<p2...

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

Ho:p1=p2Ho:p1=p2
H1:p1<p2H1:p1<p2

You obtain 33.7% successes in a sample of size n1=718n1=718 from the first population. You obtain 42.5% successes in a sample of size n2=414n2=414 from the second population.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
• There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
• The sample data support the claim that the first population proportion is less than the second population proportion.
• There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.

The statistical software output for this problem is :

Test statistics = -2.954

P-value = 0.0016

The p-value is less than (or equal to) α

reject the null

There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.

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